Abstract view
Classification of Certain Simple $C^*$Algebras with Torsion in $K_1$


Published:20011201
Printed: Dec 2001
Abstract
We show that the Elliott invariant is a classifying invariant for the
class of $C^*$algebras that are simple unital infinite dimensional
inductive limits of finite direct sums of building blocks of the form
$$
\{f \in C(\T) \otimes M_n : f(x_i) \in M_{d_i}, i = 1,2,\dots,N\},
$$
where $x_1,x_2,\dots,x_N \in \T$, $d_1,d_2,\dots,d_N$ are integers
dividing $n$, and $M_{d_i}$ is embedded unitally into $M_n$.
Furthermore we prove existence and uniqueness theorems for
$*$homomorphisms between such algebras and we identify the range of
the invariant.
MSC Classifications: 
46L80, 19K14, 46L05 show english descriptions
$K$theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] $K_0$ as an ordered group, traces General theory of $C^*$algebras
46L80  $K$theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 19K14  $K_0$ as an ordered group, traces 46L05  General theory of $C^*$algebras
